Yan L. Numerical Methods for Differential Equations

Cengage Learning, 2001, 850 pp. , 7 edition. Mathematical preliminaries. solutions of equations in one variable. interpolation and polynomial approximation. numerical differentiation and integration. initial-Value problems for ordinary differential equations. direct methods for solving linear systems. iterative techniques in matrix algebra. approximation theory. approximating eigenvalues. numerical solutions of nonlinear systems of equations. bou...

John Wiley & Sons Ltd, 2003. – 440 pages. This book represents an attempt to modernize and expand the previous volume 'The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods'. It is more modern in that it considers several topics that had not yet emerged as important research areas when the former book was written. It is expanded in that it contains a comprehensive treatment of linear multistep metho...

John Wiley & Sons, 2008, 482 p. , second edition. Authored by one of the world's leading authorities on numerical methods, this update of one of the standard references on numerical analysis outlines recent developments in the field and presenting a detailed overview of the area. The only book to provide both a detailed treatment of Runge-Kutta methods and a thorough exposition of general linear methods, it also provides practical guidance o...

Academic Press, 1991. - 344 pages. Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places...

Springer, 2010. - 268 pages. Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlig...

Springer, 1995. - 636 pages. The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE and then applications as well as the numerical methods for dealing wit...

Wiley-Interscience, 1999. - 677 pages. Incorporates the essential elements of all the numerical methods currently used in the solution of partial differential equations encountered in science and engineering. Considers partial differential equations by their type (parabolic, elliptic, or hyperbolic), and applies all relevant numerical schemes to each type. All material included is presented free of specialized notation and terminology.

Wiley, 2011. - 512 pages. A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs,...

Elsevier Science & Technology, 1983. - 688 Pages. Six invited papers on computational methods of solving partial differential equations were presented at the 1981 Conference on Numerical Solutions of Partial Differential Equations held at the University of Melbourne, Australia. They were also printed as part of the Conference Proceedings titled Numerical Solutions of Partial Differential Equations, edited by J. Noye and published by the Nort...

Springer, 2009. - 619 Pages. In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underl...